First, I don't think we can prove that every echo is human. We don't know exactly how her echoes are produced. For all we know, there could be Gallefreyan echoes, Sontaran echoes, Androgummy echoes and who knows what else.
But, for the sake of argument, let's pretend that they are. Let's assume that each of Clara's echoes are physically identical clones. Let's assume that they're all born to human parents in unsurprising ways. Then the question is "how could a post-War human being end up on pre-War Gallifrey?"
Well, baring extraordinary circumstances, nothing from a post-War timeframe can end up on a pre-War Gallifrey. The extraordinary circumstance in this case is that the Doctor's personal history extends to pre-War Gallifrey. The echo can make it to that place and time through that established conduit. Many of her echoes must be pre-War humans.
But, in the general case, how does a pre-War human end up on pre-War Gallifrey? By TARDIS, most likely (or did we call them SIDRATs in that era?) Pre-War, very few Time Lords did the gallivanting about, rebel-without-a-cause renegade thing. Very few -- but more than just the Doctor himself. She could have been the companion of the Mad Monk, or the Corsair, or the Rani, or the Master, or any other Renegade Lord.
This doesn't seem far-fetched. It almost seems inevitable. The echoes of the Great Intelligence are all dedicated to giving the Doctor an endless series of really bad days. At least some of them would try to nudge any of these Rival Renegades into the Doctor's way. The simplest method for nudging them back out of the way is to give them distracting Companions.
I think at least one Clara had to become an earlier Renegade's Companion, and she was just left to her own devices in the repair bay long enough to recommend Sexy as a TARDIS worth stealing. I figure she also caused a big enough distraction to keep that Renegade from following the Doctor and prematurely ending his career, in spite of whatever the GI did to put the Rival Renegade on the Doctor's heels.